Suppose that there are nine students in a discrete math class at a small college.

a) Show that the class must have at least 5 males or 5 females. Assuming the worse case we try to prove it wrong by alternating male and female
male - female - male - female - male - female - male - female - male
Other case:
female - male - female - male - female - male - female - male - female
Thus it is always true